The present invention relates generally to ferroelectric materials, and specifically to a system for producing structured domains in the materials.
FIG. 1 is a schematic diagram of two types of collinear ferroelectric, as are known in the art. A ferroelectric is a material which, by virtue of the material""s underlying crystal structure, is able to maintain an electric polarization, or dipole moment, in the absence of an electric field. The ferroelectric may be in the form of a mono-domain 20, wherein the ferroelectric has one polarization direction, or a multi-domain 22, wherein the crystal has many domain regions, each domain having a different direction of polarization. Mono-domain ferroelectrics are well known as materials exhibiting useful properties such as piezoelectricity and electro-optical qualities. While irregular multi-domain ferroelectrics are not considered as particularly useful, multi-domain ferroelectrics where the multi-domains have a definite structure, termed domain engineered structures (DESs), have been found to have extremely useful properties.
The polarization of a single domain in collinear ferroelectrics may be in one of two directions, at 180xc2x0 to each other. When a single domain is formed, the polarization of the domain will form spontaneously in one of the directions. The initial direction may be influenced during formation of the domain, for instance in a process termed poling wherein an electric field is applied as the ferroelectric material forms. Once formed, the polarization of the domain may be altered by further poling applications of the electric field. Typically, in the absence of an electric field, a multi-domain ferroelectric forms with the domains randomly oriented, giving an overall polarization close to or equal to zero, since this is the most stable energy state of the multi-domain.
FIG. 2 is a hysteresis curve for a multi-domain ferroelectric, plotting polarization P vs. electric field E, as is known in the art. As the electric field strength is increased, the domains of the ferroelectric start to align in a positive direction giving rise to a rapid increase in the overall polarization (OB). At very high field levels, the polarization reaches a saturation value (Psat), where all the multi-domains are substantially aligned in the positive direction. As the external field is reduced, the polarization reduces as some of the domains change alignment, but the polarization does not fall to zero when the external field is removed.
At zero external field, the domains remain aligned in the positive direction, hence the ferroelectric will show a remanent polarization Pr, The ferroelectric cannot be completely depolarized until a field of magnitude OF is applied in the negative direction. The external field needed to reduce the polarization to zero is termed the coercive field strength Ec. If the field is increased to a more negative value, the direction of polarization reverses, and if the field is increased sufficiently in the negative direction, the ferroelectric again reaches saturation. The value of the spontaneous polarization Ps (OS) is obtained by extrapolating the saturation curve onto the polarization axes. Ps is the polarization that the multi-domain ferroelectric would have, in the absence of an external field, if all the domains were aligned.
FIG. 3 is a schematic diagram of domain engineered structures and graphs of their properties, as are known in the art. DES 24 comprises two head-to-head domains formed in a rectangular plate of LiNbO3 with dimensions (x, y, z). A graph 26 shows the acoustic impedance vs. frequency for acoustic vibrations of DES 24. A graph 28 gives the impedance response for acoustic vibrations of a mono-domain crystal 25 of LiNbO3 having the same dimensions as DES 24, showing resonances dependent on the values of x, y and z. It is seen that these resonances are absent in DES 24. Conversely, two xe2x80x9cbendingxe2x80x9d resonances are present in DES 24 which are not present in the mono-domain crystal.
DES 30 has a linear periodic structure where alternating domains have opposite polarizations. Structures such as DES 30 allow, for example, second harmonic generation and optical parametric oscillation for electromagnetic waves incident on the structure, because of the non-linear properties of the alternating domains of the DES. More detailed descriptions of properties and methods of production of structures such as DES 24 and DES 30 are given in an article entitled xe2x80x9cFerroelectric Domain Engineering for Quasi-Phase-Matched Nonlinear Optical Devicesxe2x80x9d by Rosenman, Skliar, and Arie, published in Ferroelectrics 1, N4, pp 1-64 (1998), which is incorporated herein by reference. Methods detailed therein, and others known in the art for producing domain engineered structures, are summarized below.
Domain engineered structures may be formed by altering the doping of a crystal during its growth. In an article entitled xe2x80x9cEnhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domainsxe2x80x9d by Feng et al., published in Applied Physics Letters 37, pg 607 (1980), which is incorporated herein by reference, the authors describe a method for varying the spontaneous polarization of growing LiNbO3 crystals by changing the doping of the crystals. The doping was changed by periodically altering the temperature of the growing crystal, which in turn altered the concentration of yttrium which was used to dope the crystals. The variation in yttrium concentration caused a periodic reversal of the polarization of the crystals, the reversal appearing through the bulk of the crystals.
Diffusion at relatively high temperatures can be used to form DESs. For example, in an article entitled xe2x80x9cBalanced phase matching in segmented KTiOPO4 waveguidesxe2x80x9d by Bierlein et al., published in Applied Physics Letters 56, pg 1725 (1990), which is incorporated herein by reference, the authors describe polarization in KTiOPO4 (KTP) crystals. By immersing the KTP crystals in molten RbNO3/Ba(NO3)2, at a temperature of about 350xc2x0 C. for approximately 1 hour, Rb+ ions exchanged with K+ ions of the KTP. The presence of the Ba2+ ions caused polarization inversion of domains at the surface of the KTP. It will be appreciated that diffusion induced DESs are substantially surface structures.
Electron beam writing may be used to form DESs. For example, in an article entitled xe2x80x9cFabrication of Domain Reversed Gratings FOR SHG in LiNbO3 by Electron Beam Bombardmentxe2x80x9d by Keys et al., published in Electronics Letters 26, pg 188 (1990), which is incorporated herein by reference, the authors describe domain polarization reversal on the negative face of a LiNbO3 crystal. It will be appreciated since the electron beams penetrate no more than some microns in depth, DESs produced by electron beam writing must be of this order of thickness.
FIG. 4 is a schematic diagram of a poling system for fabrication of DESs, as is known in the art. A mono-domain ferroelectric 40 has a periodic dielectric photo-resist 42 applied to an upper surface of the ferroelectric. A first conductor 44 is overlaid on photo-resist 42 and the upper surface, and a second conductor 46 is applied to a lower surface of the ferroelectric. A high-voltage pulse is applied between the two electrodes. The pulse reverses the polarization of the ferroelectric in regions where the first conductor contacts the ferroelectric. This technique, and similar ones using liquid electrodes, have been used to form periodic DESs having thicknesses in a range of 0.5-3 mm, and with periods between 3.4 and 39 microns.
Scanning force microscopy (SFM) is a method known in the art for imaging surfaces, and also for modification of domain structures of thin films of ferroelectrics. A review of SFM is provided in an article entitled xe2x80x9cNanoscale Scanning Force Imaging of Polarization Phenomenon in Ferroelectric Thin Filmsxe2x80x9d by Auciello et al., published in The Annual Review of Material Sciences 28, pgs 33-41 (1998), which is incorporated herein by reference. The review includes a description of contact and non-contact SFM. In both types of SFM, a tip-electrode is scanned across the surface of a sample to be imaged, and forces exerted on the tip by the sample enable ferroelectric domains within the sample to be imaged.
FIG. 5 is a schematic diagram of a scanning force microscope (SFM) 50, as described in an article entitled xe2x80x9cFerroelectric domain switching in tri-glycine sulphate and barium-titanate bulk crystals by scanning force microscopyxe2x80x9d by Eng et al., published in Applied Physics A 66, S679-S683 (1998), which is incorporated herein by reference. In the article the authors describe how microscope 50 may be used to form DESs. A tip-electrode 52, supported by a cantilever 62, is scanned relative to an upper surface 54 of a ferroelectric sample 56. Tip-electrode 52 ends in an extremely sharp point, so that very high electric fields are generated at the tip. The height of tip-electrode 52 above the surface is maintained at a substantially fixed distance, of the order of nanometers, by circuitry 58. Circuitry 58 comprises a function generator 64 which provides an alternating potential U1 of amplitude 10 V and frequency 20 kHz that is applied to the tip-electrode, causing cantilever 62 to oscillate vertically. The vertical oscillations of the cantilever are detected by a 2-quadrant photo-detector 51, which receives a laser beam after reflection from the cantilever. An output of the photo-detector is input to an amplifier 53, which outputs a negative feedback signal to a z-positioner 55.
Sample 54 is supported on a counter-electrode 60, which may be set to a potential U2 of 60 V for a certain exposure time xcfx84, enabling domain-forming electric field pulses to be applied to sample 56. Using this technique, DESs having a lifetime of more than 5 days were formed in 125 micron thick BaTiO3. However, in 700 micron thick tri-glycine sulphate (TGS), the domains had a lifetime of only 30 minutes.
In chapter 4 of Principles and Applications of Ferroelectric and Related Materials, by Lines et al., published by The Clarendon Press, Oxford (1977), which is incorporated herein by reference, the authors describe a three-stage process for the production of a ferroelectric domain in a ferroelectric material which is already spontaneously polarized. This process also leads to the formation of domains in the scanning process of SFM 50. In a first stage, a nucleus of a primary domain is formed by an applied field opposite in direction to the spontaneous polarization. A local value of the applied field must be larger than a coercive field of the material. In a second stage, the nucleus grows in a forward and sideways direction. In a third stage, secondary domain nuclei generate at the domain wall of the primary nucleus. A switching time xcfx84sw for complete reversal of the initial spontaneous polarization is given by
xcfx84sw=xcfx84nucl+xcfx84forw xe2x80x83xe2x80x83(1) 
wherein xcfx84nucl is a time for the primary domain nucleus to be formed, and xcfx84forw is a time for the forward/sideways growth to occur.
The authors describe a method using pulsed polarization reversal for evaluating xcfx84sw. (The method is described in more detail in chapter 7 of Ferroelectricity by Fatuzzo and Merz, published by North-Holland Publishing Company (1967), which is incorporated herein by reference.) The method may also be used to produce a DES, and it is stated that for complete polarization reversal, a duration xcfx84dur of a DC pulse generating the DES must satisfy the following equation:
xcfx84dur greater than xcfx84sw xe2x80x83xe2x80x83(2) 
Providing that equation (2) is satisfied, no back-switching effect or instability is present in the formed DES.
It is an object of some aspects of the present invention to provide apparatus and a method for generating stable domain-engineered structures (DESs) in thick ferroelectric materials.
In a preferred embodiment of the present invention, a scanning probe apparatus, preferably implemented from a scanning force microscope (SFM), comprises a grounded tip-electrode, supported by a cantilever, and a counter-electrode which is coupled to operate at potentials of the order of tens of kilovolts. By grounding the tip-electrode, any instrumentation coupled to the cantilever, which in prior art scanning probe apparatus would be adversely affected if a high voltage were applied to the tip-electrode, is protected from adverse effects. By applying a high potential to the counter-electrode, high electric fields can be applied to a ferroelectric sample positioned between the electrodes. Since the electrodes of the apparatus are able to support potential differences between themselves of the order of kilovolts, the electrodes may be separated by distances of the order of millimeters and still produce average fields of the order of kV/cm. Fields of these strengths are sufficient to form stable DESs in the ferroelectric sample, including bulk samples having thicknesses of the order of several millimeters. By contrast, scanning probe apparatus known in the art, with non-grounded tip electrodes, are capable of forming DESs only in thin layers, with poor stability over time.
In an alternative preferred embodiment of the present invention, the tip-electrode is not grounded. The tip-electrode and any instrumentation coupled to the cantilever are insulated from the ground so that high voltage applied to the tip-electrode does not cause adverse effects. The counter-electrode is preferably grounded. Alternatively, the counter-electrode is insulated from the ground. As described above, high electric fields can be applied to a ferroelectric sample positioned between the electrodes by applying appropriate potentials to the tip-electrode (when the counter-electrode is grounded) or to both electrodes.
The cantilever holds the tip-electrode so that it touches, or is held at a short distance abovexe2x80x94typically less than a nanometerxe2x80x94an upper surface of the ferroelectric sample. To form DESs in the sample, the tip-electrode and the ferroelectric sample are scanned relative to each other at a substantially fixed velocity. Preferably, in order to perform the scanning, a piezoelectric positioner is coupled to the counter-electrode, and is used to pre-position and scan the ferroelectric sample in one or two horizontal dimensions relative to the tip-electrode. Alternatively or additionally, the scanning is performed by one and/or two dimensional scanning instrumentation coupled to the cantilever. The high voltage applied between the electrodes may be applied as a substantially steady DC voltage or as a pulsed DC voltage. Thus, DESs of virtually any design may be constructed in the bulk ferroelectric, including both one-dimensional (stripes) and two-dimensional patterns.
In some preferred embodiments of the present invention, the scanning is performed within a range of pre-determined xe2x80x9cdomain-writingxe2x80x9d velocities. Operating within this range, domains which are stable over time, and which are well-defined dimensionally so that there is substantially no broadening or narrowing of the domains, are developed within the bulk ferroelectric material by a substantially continuous writing process.
The tip-electrode preferably terminates at one extremely sharp point. Alternatively, in some preferred embodiments of the present invention, multi-tip electrodes, comprising two or more substantially similar point tips, are used in place of the single tip-electrode, so that multiple DESs can be written in parallel. In other preferred embodiments of the present invention, one- or two-dimensioned tip-electrodes are used, enabling DESs to be formed in the bulk ferroelectric sample by a process similar to xe2x80x9cbrandingxe2x80x9d or xe2x80x9cstampingxe2x80x9d of the sample.
In some preferred embodiments of the present invention, the scanning probe apparatus is convertible to an SFM, the SFM being able to read DESs formed by the apparatus.
There is therefore provided, according to a preferred embodiment of the present invention, scanning probe apparatus, including:
a tip-electrode which is coupled to be held at a substantially ground potential;
a counter-electrode which is positioned in proximity to the tip-electrode;
a voltage source, coupled to maintain the counter-electrode at a non-ground potential; and
positioning-instrumentation, which is adapted to maintain the tip-electrode at a suitable position relative to a surface of a ferroelectric sample located in a space between the tip-electrode and the counter-electrode so as to generate an electric field in the ferroelectric sample greater than a coercive field thereof.
Preferably, the apparatus includes scanning-instrumentation which is adapted to induce the tip-electrode and the ferroelectric sample to move relative to each other, so that the tip-electrode scans across the surface of the sample.
Further preferably, the scanning-instrumentation is adapted to induce relative motion between the tip-electrode and the ferroelectric sample at a suitable velocity to produce a stable domain-engineered structure (DES) having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the DES includes a one-dimensional DES.
Alternatively, the DES includes a two-dimensional DES.
Preferably, the suitable velocity includes a critical relative velocity having a magnitude Vcrit approximately equal to R/xcfx84sw, wherein R is a domain nuclear radius produced by the electric field and xcfx84sw is a switching time for reversal of a polarization of the ferroelectric sample.
Preferably, the voltage source is adapted to maintain the non-ground potential at a value URmin approximately equal to or greater than a product of the coercive field and a thickness of the ferroelectric sample.
Further preferably, the voltage source is adapted to pulse the non-ground potential for a pre-determined period xcfx84dur so as to produce a stable DES having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the DES includes a one-dimensional DES.
Alternatively, the DES includes a two-dimensional DES.
Preferably, the pre-determined period xcfx84dur is greater than a switching time xcfx84sw for reversal of a polarization of the ferroelectric sample and is less than a dielectric relaxation time xcfx84rel of the ferroelectric sample.
Preferably, the apparatus includes an insulating holder which is adapted to hold the ferroelectric sample and to electrically insulate the counter-electrode.
Further preferably, the insulating holder includes a heater which is adapted to maintain a temperature of the ferroelectric sample above an ambient temperature of the apparatus.
Alternatively or additionally, the insulating holder includes a cooler which is adapted to maintain a temperature of the ferroelectric sample below an ambient temperature of the apparatus.
Preferably, the tip-electrode terminates in two or more separate sharp points, and the electric field includes substantially similar respective electric fields generated by each point.
Alternatively, the tip-electrode terminates in a multi-dimensional surface.
Further alternatively, the tip-electrode terminates in a single sharp point.
Preferably, the voltage source is adapted to generate a sufficient potential so as to form one or more stable domains in the ferroelectric sample.
Preferably, the one or more stable domains include a one-dimensional DES having a substantially invariant cross-section throughout the sample.
Alternatively or additionally, the one or more stable domains include a two-dimensional DES having a substantially invariant cross-section throughout the sample.
Preferably, the ferroelectric sample includes an optical waveguide.
Preferably, the one or more stable domains include a periodic DES.
Alternatively, the one or more stable domains include an aperiodic DES.
Preferably, the ferroelectric sample includes an existing DES, and the voltage source is adapted to apply a potential so as to erase at least a part of the existing DES.
Preferably, the positioning-instrumentation is adapted to maintain the position of the tip-electrode to be substantially in contact with the surface of the ferroelectric sample.
Preferably, the tip-electrode, the counter-electrode, the voltage source, and the positioning-instrumentation are adapted to be operative as a scanning force microscope which reads the ferroelectric sample.
There is further provided, according to a preferred embodiment of the present invention, scanning probe apparatus, including:
a tip-electrode which is coupled to be maintained at a first potential;
a counter-electrode which is positioned in proximity to the tip-electrode and which is coupled to be maintained at a second potential differing from the first potential; and
scanning-instrumentation, which is adapted to induce relative motion between the tip-electrode and a ferroelectric sample located in a space between the tip-electrode and the counter-electrode at a suitable velocity to produce a stable domain-engineered structure (DES) having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the suitable velocity includes a critical relative velocity having a magnitude Vcrit approximately equal to R/xcfx84sw, wherein R is a domain nuclear radius produced by an electric field generated in the ferroelectric sample by the first and second potential and xcfx84sw is a switching time for reversal of a polarization of the ferroelectric sample.
Preferably, an electric field generated in the ferroelectric sample by the first and second potential is greater than a coercive field thereof.
There is further provided, according to a preferred embodiment of the present invention, scanning probe apparatus, including:
a tip-electrode which is coupled to be maintained at a first potential;
a counter-electrode which is positioned in proximity to the tip-electrode and which is coupled to be maintained at a second potential differing from the first potential by a value greater than approximately 150 V; and
positioning-instrumentation, which is adapted to maintain the tip-electrode at a suitable position relative to a surface of a ferroelectric sample located in a space between the tip-electrode and the counter-electrode so as to generate an electric field in the ferroelectric sample greater than a coercive field thereof.
Preferably, the apparatus includes scanning-instrumentation which is adapted to induce the tip-electrode and the ferroelectric sample to move relative to each other, so that the tip-electrode scans across the surface of the sample.
Further preferably, the scanning-instrumentation is adapted to induce relative motion between the tip-electrode and the ferroelectric sample at a suitable velocity to produce a stable domain-engineered structure (DES) having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the DES includes a one-dimensional DES.
Alternatively, the DES includes a two-dimensional DES.
Preferably, the suitable velocity includes a critical relative velocity having a magnitude Vcrit approximately equal to R/xcfx84sw, wherein R is a domain nuclear radius produced by the electric field and xcfx84sw is a switching time for reversal of a polarization of the ferroelectric sample.
Preferably, a difference between the first and the second potential is set at a value URmin approximately equal to or greater than a product of the coercive field and a thickness of the ferroelectric sample.
Further preferably, the difference is pulsed for a pre-determined period xcfx84dur so as to produce a stable DES having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the DES includes a one-dimensional DES.
Alternatively, the DES includes a two-dimensional DES.
Preferably, the pre-determined period xcfx84dur is greater than a switching time xcfx84sw for reversal of a polarization of the ferroelectric sample and is less than a dielectric relaxation time xcfx84rel of the ferroelectric sample.
Preferably, the apparatus includes an insulating holder which is adapted to hold the ferroelectric sample and to electrically insulate the counter-electrode.
Preferably, the tip-electrode terminates in two or more separate sharp points, and the electric field includes substantially similar respective electric fields generated by each point.
Preferably, the tip-electrode terminates in a multi-dimensional surface.
Alternatively, the tip-electrode terminates in a single sharp point.
Preferably, the voltage source is adapted to generate a sufficient potential so as to form one or more stable domains in the ferroelectric sample.
Preferably, the one or more stable domains include a one-dimensional DES having a substantially invariant cross-section throughout the sample.
Alternatively, the one or more stable domains include a two-dimensional DES having a substantially invariant cross-section throughout the sample.
Preferably, the ferroelectric sample includes an optical waveguide.
Preferably, the one or more stable domains include a periodic DES.
Alternatively, the one or more stable domains include an aperiodic DES.
Preferably, the ferroelectric sample includes an existing DES, and the apparatus is adapted to erase at least a part of the existing DES.
Further preferably, the positioning-instrumentation is adapted to maintain the position of the tip-electrode to be substantially in contact with the surface of the ferroelectric sample.
Preferably, the tip-electrode, the counter-electrode, and the positioning-instrumentation are adapted to be operative as a scanning force microscope which reads the ferroelectric sample.
There is further provided, according to a preferred embodiment of the present invention, a method for forming a domain-engineered structure (DES) in a ferroelectric sample, including:
maintaining a tip-electrode at a substantially ground potential;
positioning a counter-electrode in proximity to the tip-electrode, so as to form a space therebetween;
applying a non-ground potential to the counter-electrode;
placing the ferroelectric sample in the space; and
positioning the tip-electrode relative to a surface of the ferroelectric sample so as to generate an electric field in the ferroelectric sample between the tip-electrode and the counter-electrode that is greater than a coercive field of the sample.
Preferably, the method includes inducing the tip-electrode and the ferroelectric sample to move relative to each other, so that the tip-electrode scans across the surface of the ferroelectric sample.
Preferably, inducing the tip-electrode and the ferroelectric sample to move relative to each other includes inducing the tip-electrode and the ferroelectric sample to move at a suitable relative velocity to produce a stable domain-engineered structure (DES) having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the DES includes a one-dimensional DES.
Alternatively, the DES includes a two-dimensional DES.
Preferably, the suitable relative velocity includes a critical relative velocity having a magnitude Vcrit approximately equal to R/xcfx84sw, wherein R is a domain nuclear radius produced by the electric field and xcfx84sw is a switching time for reversal of a polarization of the ferroelectric sample.
Preferably, applying the non-ground potential includes applying a potential at a value URmin approximately equal to or greater than a product of the coercive field and a thickness of the ferroelectric sample.
Further preferably, applying the potential includes pulsing the non-ground potential for a pre-determined period xcfx84dur so as to produce a stable DES having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably, the DES includes a one-dimensional DES.
Alternatively, the DES includes a two-dimensional DES.
Preferably, the pre-determined period xcfx84dur is greater than a switching time xcfx84sw for reversal of a polarization of the ferroelectric sample and is less than a dielectric relaxation time xcfx84rel of the ferroelectric sample.
Preferably, the method includes maintaining a temperature of the ferroelectric sample different from an ambient temperature of the apparatus.
Further preferably, the method includes terminating the tip-electrode in two or more separate sharp points, so that the electric field includes substantially similar respective electric fields generated by each point.
Preferably, the method includes terminating the tip-electrode in a multi-dimensional surface.
Alternatively, the method includes terminating the tip-electrode in a single sharp point.
Preferably, the method includes forming one or more stable domains in the ferroelectric sample.
Preferably, the one or more stable domains include a one-dimensional DES having a substantially invariant cross-section throughout the sample.
Alternatively, the one or more stable domains include a two-dimensional DES having a substantially invariant cross-section throughout the sample.
Preferably, the ferroelectric sample includes an optical waveguide.
Preferably, the one or more stable domains include a periodic DES.
Alternatively, the one or more stable domains include an aperiodic DES.
Preferably, the ferroelectric sample includes an existing DES, and the method includes erasing at least a part of the existing domain.
Preferably, positioning the tip-electrode includes placing the tip-electrode to be substantially in contact with the surface of the ferroelectric sample.
Preferably, the tip-electrode and the counter-electrode are adapted to be operative as a scanning force microscope which reads the ferroelectric sample.
There is further provided, according to a preferred embodiment of the present invention, a method for forming a domain-engineered structure (DES) in a ferroelectric sample, including:
maintaining a tip-electrode at a first potential;
positioning a counter-electrode in proximity to the tip-electrode, so as to form a space therebetween;
placing the ferroelectric sample in the space; and
setting the counter-electrode at a second potential, different from the first potential, so that a difference between the first and the second potential is a value greater than approximately 150 V.
There is further provided, according to a preferred embodiment of the present invention, scanning probe apparatus, including:
a tip-electrode which is coupled to be held at a first potential;
a counter-electrode which is positioned in proximity to the tip-electrode;
a voltage source, coupled to maintain the counter-electrode at a second potential so as to generate an electric field between the tip-electrode and the counter-electrode; and
positioning-instrumentation, which is adapted to maintain the tip-electrode at a suitable position relative to a surface of a ferroelectric sample located in a space between the tip-electrode and the counter-electrode so that the electric field is greater than a coercive field of the ferroelectric sample and forms one or more stable domains in the ferroelectric sample, each domain having a substantially invariant cross-section throughout the sample.
There is further provided, according to a preferred embodiment of the present invention, a method for forming a domain-engineered structure (DES) in a ferroelectric sample, including:
maintaining a tip-electrode at a first potential;
positioning a counter-electrode in proximity to the tip-electrode so as to form a space therebetween;
placing the ferroelectric sample in the space;
setting the counter-electrode at a second potential differing from the first potential; and
inducing relative motion between the tip-electrode and the ferroelectric sample at a suitable velocity to produce a stable domain-engineered structure (DES) having a substantially invariant cross-section throughout the ferroelectric sample.
Preferably the method includes the first and second potential generating an electric field in the ferroelectric sample greater than a coercive field thereof.
Preferably, the suitable velocity includes a critical relative velocity having a magnitude Vcrit approximately equal to R/xcfx84sw, wherein R is a domain nuclear radius produced by an electric field generated in the ferroelectric sample by the first and second potential and xcfx84sw is a switching time for reversal of a polarization of the ferroelectric sample.
The present invention will be more fully understood from the following detailed description of the preferred embodiment thereof, taken together with the drawings, in which: